1. lip, verge. Rim,brim refer to the boundary of a circular or curved area. A rim is a line or surface bounding such an area; an edge or border: the rim of a glass.Brim usually means the inside of the rim, at the top of a hollow object (except of a hat), and is used particularly when the object contains something: The cup was filled to the brim.

rim

n.

Old English rima "edge, border, verge, coast," as in særima "seashore," literally "rim of the sea," and dægrima "dawn," literally "rim of the day." Related to Old Norse rime, rimi "a raised strip of land, ridge," Old Frisian rim "edge," but with no other known cognates. The snare drummer's rim shot (striking the rim and the head at once) is recorded from 1934.